MadsenLab

Over the last few months, a high-profile controversy has been brewing in evolutionary biology. Martin Nowak, Corina Tarnita, and E.O. Wilson published “The Evolution of Eusociality” in Nature, in which they apply Nowak and Tarnita’s work on evolutionary set theory to the evolution of cooperation and particularly eusociality among the social insects. What made this work controversial is their claim that such an approach renders inclusive fitness theory unncessary. But what got legions of evolutionary biologists (including Alan Grafen) really hot under the collar was the additional suggestion that inclusive fitness makes enough simplifying assumptions that it doesn’t even apply to the empirical cases which it is purported to best explain, potentially calling into question a great deal of work based on IF theory.

I’m not qualified to evaluate the latter claims, which is fine because Alan Grafen and Richard Dawkins are on the warpath and I’m sure we’ll see a paper in response quite soon.

I’m more interested in the general claim, that the approach taken by Nowak et al. represents a useful and general way of looking at evolution in realistically structured populations. Because I think they’re on the right track. The last thirty years have seen an explosion of evolutionary models for populations structured in various ways, because virtually everyone now realizes the stability of cooperative phenomena depend crucially upon assortative interaction.  In other words, structured interaction helps keep defectors from invading groups of mutually supporting cooperators.  Some such groups are kin-based, others are based upon social network connections, and still other groupings are spatial.  All of these situations can be described by understanding evolutionary dynamics upon generalized networks or graphs (since spatial lattices are simply regular graphs).

And understanding the effect of complex and rich structure upon evolutionary dynamics is critical, as a growing mountain of theoretical work has shown. We started understanding evolution in quantitative, dynamical system terms (with the work of Wright and Fisher), by largely ignoring interaction structure (although Wright did some crucial early work on assortative mating). Theoretical biologists employed what physicists call a “mean-field approximation,” assuming that every organism if a population is equally likely to reproduce with any other, and thus evolutionary forces can be treated as an average “field” applied to the state of the population as a whole.¹ Nearly every equation you see in a basic text on population genetics is a mean-field model. The same is true for quantitative models of social learning ² Boyd and Richerson’s (1985) landmark book is filled with mean-field models, and quite understandably so.  Mean-field models are where we typically start trying to understand a complex phenomenon.

Over the last decade or more, Martin Nowak and his group have been key contributors to understanding how the dynamics of evolutionary processes depend upon relaxing the mean-field approximation and incorporating explicitly the structure of interaction into our models.  But even what we now call “complex” network models tend to represent only a single type of relationship between individuals. The “complex” moniker here refers to topology, not richness of association or relationship. So I find Nowak and Tarnita’s work on “evolutionary set theory” quite interesting, as a generalization of the network concept (and which clearly can interoperate with it).  In this posting, I want to explore where such an approach leads, in terms of the structure of evolutionary models, and what methods will be required to analyze those models as we add realism and complexity.